As observed in [1]} section \(2.2\) , \(\Sigma (C)\)  is a tropical curve parameterized by the generalized cone complex \(\Sigma (S)\) , and \(\Sigma (C^\circ )\)  is a puncturing of \(\Sigma (C)\) . For each cone of \(\sigma \in \Sigma (S)\) , we have an induced family of tropical maps \(\Gamma _\sigma ^\circ \rightarrow \Sigma (X)\)  of a fixed tropical type \(\tau _\sigma \) . The cone \(\sigma \in \Sigma (S)\)  is associated with a stratum of \(S_\sigma \subset S\) , and we say the family of punctured log maps restricted to \(S_\sigma \)  has tropical type \(\tau _{\sigma }\) .
